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Commit d5c38e00 authored by Laurence Viry's avatar Laurence Viry
Browse files

MaJ Multidim

parent e084f2fa
......@@ -1288,6 +1288,7 @@
"source": [
"### Interprétation\n",
"\n",
"<img src=\"../../figures/StructNoise.jpg\",width=\"80%\",height=\"60%\">\n",
"#### Percentage of inertia - Choice of number of axes\n",
"\n",
"* Percentage of information explained by each axis (eigenvalue)\n",
......@@ -1296,20 +1297,9 @@
},
{
"cell_type": "code",
"execution_count": 13,
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"outputs": [],
"source": [
"barplot(temperat.pca$eig[,2])"
]
......@@ -1370,20 +1360,20 @@
"metadata": {},
"source": [
"#### Eléments supplémentaires ou illustratifs\n",
"Additional items may be ** individuals ** and / or ** variables **. They are not used to calculate distances between individuals or to construct the correlation matrix.<br/>\n",
"Supplementary items may be ** individuals ** and / or ** variables **. They are not used to calculate distances between individuals or to construct the correlation matrix.<br/>\n",
"<br/>\n",
"$\\Longrightarrow$ ** they do not participate in the construction of the axes **, they are a help to their interpretation. <br/>\n",
"<br/>\n",
"* <FONT color=\"#013ADF\">Additional variables</FONT><br/>\n",
"* <FONT color=\"#013ADF\">Supplementary variables</FONT><br/>\n",
" - *Quantitative variables* : they will be projected on the circle of correlation. <br/>\n",
" The coordinate of the additional variable $X^{j}$ on the k-axis is the correlation between this variable and the factor $F^{k}$.<br/>\n",
" <br/>\n",
" - *Qualitative variables* : projection of each modality ** to the barycenter of the individuals associated with this modality **, on ** the graph of the individuals **<br/>\n",
" - *Categorical variables* : projection of each modality ** to the barycenter of the individuals associated with this modality **, on ** the graph of the individuals **<br/>\n",
" <br/>\n",
"\n",
" The information can be * represented in the form of a color code *, individuals associated with the same category are colored in the same color.<br/>\n",
"<br/>\n",
"* <FONT color=\"#013ADF\">Additional individuals </FONT>: they are projected on the graph of the individuals."
"* <FONT color=\"#013ADF\">Supplementary individuals </FONT>: they are projected on the graph of the individuals."
]
},
{
......@@ -1416,11 +1406,13 @@
"<br/>\n",
"* <FONT color=\"#013ADF\">Quantitatives variables</FONT> : $(r(V^{j},F^{k}), j=1 \\ldots p)$<br/>\n",
" <br/>\n",
" - Variables that have a correlation coefficient with the factor are kept significantly.<br/>\n",
"<br/>\n",
" - For each axis, we sort the variables of the highest correlation coefficient at least high.<br/>\n",
" - Correlation between each variable and the principal component of rank s is calculated.<br/>\n",
" - Correlation coefficients are sorted and significant ones are output. <br/>\n",
"<br/>\n",
"* <FONT color=\"#013ADF\">Qualitative variable</FONT> : an analysis of variance is performed for each qualitative variable and each factor (Fisher test, Student test).\n"
"\n",
"* <FONT color=\"#013ADF\">Categorical variable</FONT> : an analysis of variance is performed for each qualitative variable and each factor :\n",
" - an F-test by variable\n",
" - for each category, a Student’s t-test to compare the average of the category with the general mean\n"
]
},
{
......@@ -1787,6 +1779,20 @@
"dimdesc(temperat.pca)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### PCA in practice\n",
"1. Choose active variables\n",
"2. Rescale (or not) the variables\n",
"3. Perform PCA\n",
"4. Choose the number of dimensions to interpret\n",
"5. Joint analysis of the cloud of individuals and the cloud of variables\n",
"6. Use indicators to enrich interpretation\n",
"7. Go back to raw data for interpretation"
]
},
{
"cell_type": "markdown",
"metadata": {},
......
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